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A gunman holds his weapon as he stands guard in Fallujah, 65 kilometers (40 miles) west of Baghdad, Iraq. Islamic militants controlling a mainly Sunni area west of Baghdad are so well-armed that they could occupy the capital, a top Iraqi official warned Monday. (AP)

BAGHDAD — Islamic militants controlling a mainly Sunni area west of Baghdad are so well-armed that they could occupy the capital, a top Iraqi official warned Monday, a frank and bleak assessment of the challenge posed in routing the insurgents as a new wave of bombings killed at least 31 people.

Since late December, members of Iraq’s al-Qaida branch — known as the Islamic State of Iraq and the Levant — have taken over parts of Ramadi, the capital of the largely Sunni western province of Anbar. They also control the center of the nearby city of Fallujah, along with other non-al-Qaida militants who also oppose the Shiite-led government.

Iraqi government forces backed by Sunni tribal militias launched an all-out offensive Sunday to seize back control of Ramadi and surrounding areas from the militants. Five government-allied tribesmen were killed in the initial fighting, and 15 tribesmen and government forces were wounded, provincial spokesman Dhari al-Rishawi said.

Fierce clashes continued Monday, with government forces and allied tribesmen struggling to advance in the face of tough resistance, according to local police.

Al-Rishawi said the al-Qaida militants are especially active at night, and are employing snipers to stop government forces from advancing.

Two policemen and a local television cameraman who had been accompanying them were killed when a roadside bomb hit their convoy inside Ramadi, police said.

An even bigger fight could lie ahead in nearby Fallujah, which like Ramadi was once a major battleground for U.S. forces.

“The weapons that were brought inside Fallujah are huge and advanced and frankly enough to occupy Baghdad,” Deputy Interior Minister Adnan al-Asadi said in a speech.

He did not elaborate on the type or quantity of the weapons, but described “fierce battles” there and in Ramadi.

Bomb attacks frequently strike Baghdad. But a military assault on the heavily guarded capital, with an estimated 7 million residents, would be far harder to pull off for an al-Qaida guerrilla force than the seizure of much smaller Fallujah.

Even so, Interior Ministry spokesman Saad Maan Ibrahim said this week’s assault in Anbar was needed to keep the fighters from trying to storm the capital itself.

“Al-Qaida in Iraq has plenty of weapons and fighters,” he said, without offering details. “If military action was not taken and if the operation by security forces was delayed for a few weeks, there would have been an assault on Baghdad.”

Sporadic clashes erupted in Fallujah Monday afternoon but had stopped by nightfall. Shops there were mainly shuttered and city streets were eerily empty as residents hunkered down or fled for safer ground. Much of the city lacks electricity, according to residents.

Two civilians were wounded in the city and a number of houses were damaged when artillery shells hit them, according to local hospital officials. It was unclear who launched the shells.

The unrest in Anbar and other mainly Sunni-dominated provinces has uprooted thousands of people from their homes as they flee the fighting.

Bassem al-Falahi, a Fallujah taxi driver whose house was damaged in the shelling, said the blast was the last straw.

“All my neighbors left the area several days ago, but I decided to stay because my house is far away from the clashes,” he said. “With today’s incident, I have decided to take my family outside Fallujah. ... I fear the worst if the final battle starts.”

Violence spiked in Iraq after the government staged a deadly crackdown on a Sunni protest camp last April. Militants have also targeted civilians, particularly in Shiite areas of Baghdad, with coordinated car bombings and other deadly attacks.

Nobody immediately claimed responsibility for Monday’s blasts. But multiple bombings against civilians and state institutions are frequently the work of the al-Qaida affiliate in Iraq, which has been emboldened by successes of its fellow militants in the civil war next door in Syria.

The deadliest strike was a parked car bomb that tore through an outdoor market south of the capital, killing seven people and wounding 13, police said. A bomb on a nearby commercial street killed two more, while another three died and seven were wounded in a southeastern district. Another bomb in a northern suburb killed three and wounded six.

Two separate car bombs near court buildings also killed seven and wounded 22, said police. Later, a car bomb went off in a commercial street in western Baghdad, killing three people and wounding nine others. And another one struck another busy street in the southwestern section of the city, killing three people and wounding 11.

Hospital officials confirmed the death tolls. Officials describing the attacks spoke on condition of anonymity because they were not authorized to talk to the media.

Separately on Monday, the European Union pledged around €75 million ($102 million) of development support to Iraq through 2020, highlighting the ongoing challenges of rebuilding the country after years of war.

The funds will go primarily toward efforts to strengthen rule of law, build up the education sector and provide sustainable energy.

“Over the past months the escalation of violence undermined its stability, but the EU is confident that the Iraqi authorities will work towards a successful transition to democracy and long term stability for the benefit of all of Iraq’s citizens,” Andris Piebalgs, the European commissioner for development, said in a statement.